Best one-sided \(L_1\) approximation to the Heaviside and sign functions

DOI10.1016/j.jat.2012.02.006zbMath1248.41013OpenAlexW2089540934MaRDI QIDQ435180

Reinaldo Martínez-Cruz, Jorge Bustamante González, José María Quesada

Publication date: 11 July 2012

Published in: Journal of Approximation Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jat.2012.02.006

zbMATH Keywords

Jacobi polynomialsHermite interpolationone-sided approximation

Mathematics Subject Classification ID

Best approximation, Chebyshev systems (41A50) Approximation by polynomials (41A10)

Related Items (12)

FRACTAL DIMENSION OF MULTIVARIATE α-FRACTAL FUNCTIONS AND APPROXIMATION ASPECTS ⋮ Best \(L_{1}\) approximation of Heaviside-type functions from Chebyshev and weak-Chebyshev spaces ⋮ Best one-sided approximation in the mean of the characteristic function of an interval by algebraic polynomials ⋮ Best \(L^1\) approximation of truncated functions, Whitney-type and Bohr-Favard-type inequalities ⋮ Optimal Hermite-Fejér interpolation of algebraic polynomials and the best one-sided approximation on the interval \([-1,1\)] ⋮ Polynomial operators for one-sided approximation to functions in \(W^r_p [0,1\)] ⋮ ONE-SIDED L-APPROXIMATION ON A SPHERE OF THE CHARACTERISTIC FUNCTION OF A LAYER ⋮ Gaussian, Lobatto and Radau positive quadrature rules with a prescribed abscissa ⋮ On Chebyshev-Markov-Krein inequalities ⋮ Quasi orthogonal Jacobi polynomials and best one-sided \(L_1\) approximation to step functions ⋮ Extremal functions with vanishing condition ⋮ Polynomial operators for one-sided \(L_p\)-approximation to Riemann integrable functions

Cites Work

• Best one-sided approximation of polynomials under \({\mathbf L}_1\) norm
• On polynomials of best one sided approximation
• One-sided approximation of a step by algebraic polynomials in the mean
• Unnamed Item

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